Question

Can you come up with the equation for the table to the left in y=m+ b form?

x 1, 2, 3, 4
y 3,5, 7, 9

Answer 1

To find the equation of the line in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \) based on the provided points.

From your data, we have the following points:
- (1, 3)
- (2, 5)
- (3, 7)
- (4, 9)

### Step 1: Calculate the slope \( m \)

The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's use the first two points: (1, 3) and (2, 5).

\[
m = \frac{5 - 3}{2 - 1} = \frac{2}{1} = 2
\]

### Step 2: Determine the y-intercept \( b \)

Now that we have the slope \( m = 2 \), we can use one of the points to find the y-intercept \( b \). We'll use the point (1, 3).

Using the equation \( y = mx + b \):
\[
3 = 2(1) + b
\]
\[
3 = 2 + b
\]
\[
b = 3 - 2 = 1
\]

### Step 3: Write the equation

Now that we have both \( m \) and \( b \), we can write the equation:
\[
y = 2x + 1
\]

So, the equation in \( y = mx + b \) form is:
\[
y = 2x + 1
\]